Consider the primal problem below. The application of the simplex method to the primal requires the use of an artificial variable in the second constraint of the standard primal to secure a starting basic solution. Show that the presence of an artificial primal in equation form variable does not affect the definition of the dual because it leads to a redundant dual constraint.
Consider the primal problem below. The application of the simplex method to the primal requires the use of an artificial variable in the second constraint of the standard primal to secure a starting basic solution. Show that the presence of an artificial primal in equation form variable does not affect the definition of the dual because it leads to a redundant dual constraint.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 73P
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Question
Consider the primal problem below. The application of the simplex method to the primal requires the use of an artificial variable in the second constraint of the standard primal to secure a starting basic solution. Show that the presence of an artificial primal in equation form variable does not affect the definition of the dual because it leads to a redundant dual constraint.
Transcribed Image Text:Maximize z = 5x₁ + 12x2 + 4x3
Subject to
Primal
Dual Problem
X1 + 2x2 + x3 ≤ 10
2X1 X2 + 3x3 = 8
X1, X2 > 0
Primal in Equation Form
Dual Variables
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